On solid ground, cavalry has a charge attack that does extra damage when they connect with an enemy, but this bonus doesn't get applied when cavalry moves up higher elevation. One of the other bonuses of being on a hill is that enemy units, like cavalry, don't get a charge bonus. This means that it's advantageous to put archers or siege engines on hills, as they have the highest vision of any unit and will be able to pelt enemies from a distance. Instead, units have an increased line of sight when on hills and higher elevations.
Fans of Age of Empires 2 will know that units get a roughly 25 percent boost when fighting enemies at a lower elevation, but Age of Empires 4 doesn't have any damage bonus.
The short answer is that, yes, Age of Empires 4 does have a hill bonus, although it doesn't work like past games.
